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\subsection{Introduction}
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        \item existing reconstruction methods suffer from different degrees of overfitting
        \item overfitting is a major obstacle in the objective analysis of cryo-EM maps
        \item overfitting may remain undetected
    \end{enumerate}
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现存的重建算法或多或少都有过拟合. 过拟合在这些算法中是不可测的. 

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        \item The high levels of noise together
        with the incompleteness of the data mean that cryoEM structures are not fully determined by the
        experimental data and therefore prone to overfitting.
    \end{enumerate}
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理论上来说, 从一个三维模型投影出各个二维图像是很容易的. 但是反过来是很难得. 因为从三维模型到二维的图像会丢失很多信息, 比如: 颗粒的图像的取向, 不同类别的划分, 等等. 
此外, 低信噪比的图像也进一步加重了这些困难. 总之, 由于高水平的噪音和数据的不完整性, cryoEM 的结构不是完全由实验数据决定的(还有很多任意开始的参数), 因而更容易过拟合. 

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        \item Ill-posed problems can be tackled by regularization, where the experimental data are complemented with external or prior information
        \item A particularly powerful
        source of prior information about cryo-EM reconstructions is smoothness.
        \item smoothness 常常应用于过滤的步骤, 即过滤高频保留低频, 这样才能 smoothness. 
        \item 但是现存的算法都是启发式算法, 这就会导致调参的任意性, 又因为人的主观性, 所以最后的电子密度图很容易过拟合. 
    \end{enumerate}
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    \begin{enumerate}
        \item Recent attention for statistical image processing
        methods could be explained by a general interest in
        reducing the amount of heuristics in cryo-EM
        reconstruction procedures. 
        \item the statistical approach
        seeks to maximize a single probability function.
        \item find the model that has the highest
        probability of being the correct one in the light of
        the observed data. 
        \item the maximum likelihood (ML)
        estimate is asymptotically unbiased and efficient. That is, in the limit of very large data sets, the ML
        estimate is as good as or better than any other
        estimate of the true model
        \item In Bayesian
        statistics, regularization is interpreted as imposing
        prior distributions on model parameters, and the
        ML optimization target may be augmented with
        such prior distributions. 
    \end{enumerate}
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最近, 使用统计学方法处理图像的目标可以解释成: 减少cryo-EM 重构步骤中的启发式数量. 即, 用统计学的方法找到一个概率密度函数的最大化. ML(Maximum Likelihood) 估计的方法是最有可能找到真实模型估计的一种方法. ML 需要大数据集, 但是在实践中没有那么大的数据量, 因此, 需要一个先验信息来作为数据集不足的补充. 